Identification of State Measurement Toolkits (Data Transmit Channels) for Stochastic and Uncertain Environments

This paper analyzes the problem of identifying state measurement toolkits or data transmit channels for highly realistic stochastic and uncertain environments in control systems or, correspondingly, communication systems. The latter can be exemplified by a Channel State Information (CSI) request. CSI is vital for many reasons. Namely, it can include specific estimates of direct and cross channels and their accuracy rate, prior to the point when transmitted vectorvalued data process is precoded for the purpose of crosstalk elimination. The solution we are presenting is based on the construction of an Adaptive Kalman Filter (AKF) that converges to the hidden Optimal Kalman Filter (OKF) without an estimate bias. This is achieved by first constructing and then minimizing a specific Auxiliary Performance Index (API), which must meet the following criteria: 1) it reaches its minimum synchronously with the Original Performance Index (OPI) that cannot be measured; 2) it is measurable and admissible for use via any practical optimization method. Our presentation of what is known as the Active Principle of Adaptation (APA) uses a general specification example, that allows for a step-by-step breakdown of the entire procedure. An experimental validation of these theoretical premises sums up the paper.